J . Phys. Chem. 1986, 90, 3217-3220 54.6 kJ/mol for that of HMS. The difference in the equilibrium constants is determined by the entropy term for which we find ASR = 98.2 f 7.6 J/(mol K-I) in the case of benzaldehyde. Comparison with our value of 57.6 for the formaldehyde-bisulfite system shows that the former is greater by a factor of about 1.7. The reason presumably is steric hindrance by the larger benzene ring. The pH dependence of the equilibrium constant is obtained by combining the equilibria 2 and 3 with eq A to express the total concentration of S(1V) species in terms of the concentrations of HS03- and hydrogen ions:
+ [HS03-] + [SOj2-]
[S(IV)] = [H2SO3]
= [HS03-]([H+]/K2
+ 1 + K,/[H+])
= [HS03-]/f
(D)
As before, we denote by KIa the equilibrium constant in the pH range 3-6 where HS03- is the dominant S(1V) ion. In this manner, K1 can be calculated from KIaand the prevailing hydrogen ion concentration. The results are shown in Figure 4 by the solid line. The experimental data points (at 25 "C) follow the calculated line quite closely, indicating that eq D represents the formaldehyde-S(1V) equilibrium reasonably well. Figure 4 includes a similar calculation for the equilibrium involving S(IV) and benzaldehyde. The rate constant for the decomposition of HMS as determined here is an effective rate constant for the sum of reactions l a and lb
k-1 = k-ia
+ k-,b[OH-]
Skrabal and SkrabalIg and Sorensen and Andersen4 have previously studied the decomposition of H M S in the alkaline pH range and found k-lb = 8.5 X lo3 M-' s-I each. At pH 5.6 one has [OH-] = 4 X M so that kqb[OH-] = 3.4 X This value has the same magnitude as the effective rate constant ob-
3217
served here, Ll = 1.1 X S-I, indicating that at pH 5.6 the decomposition of H M S still proceeds primarily via reaction 1b. Kok et al.,17who studied the decomposition of H M S at pH 4 and 5, reported the effective rate coefficients at 25 "C to be 4.8 X and 3.5 X 10" S-I, respectively. Their values agree within a factor of 2 with the rate coefficients expected if reaction 1 b were rate determining. If one assumes that may be ignored at pH L 4, one finds from the data given by Kok et aL17 and from our own value at pH 5.6 an average k-lb = (3.7 f 1) X lo3. This is by a factor of 2.3 lower than the values of Skrabal and SkrabalIg and of Sorensen and A n d e r ~ e n but , ~ otherwise self-consistent. Accordingly, we conclude that in the pH range greater than pH 4 reaction 1 b is dominant. If we have reported our equilibrium constants in terms of HS03-, it was mainly because this is the major S(1V) species in the pH range 3-6 and because it is the species that was measured. Boyce and HoffmannZohave studied the rate of formation of HMS from formaldehyde and S(1V) in the pH region C-3.4. They found bisulfite to be the principal reactant at pH C 2, whereas above this value sulfite had to be included as a reactant. According to their data the formation of HMS occurs at about the same rate via both channels of reaction 1 when the pH is near 2.7. In this situation, and assuming equilibrium, the equal rates should also occur for the two reverse reactions. At pH 2.7 the concentrations of OH- is 5 X M. We thus estimate kla k-lb, 5 X = 1.9 X s-l and kla = Klak-,, = 0.07 M-' s-'. Boyce and Hoffmann20 reported kla = 0.43 M-' s-' which is by a factor of 6 greater. However, Kok et al.I7 noted that their own results at pH 4 for the effective forward rate coefficient k , was by a factor of 4 lower than that of Boyce and Hoffmann20 when extrapolated from pH 3.4 to pH 4. Thus, it appears that the rate constant values of Boyce and Hoffmann near pH 3 are slightly too high. Nevertheless, the data of Boyce and Hoffmann,20 Kok et al.,17 and the present results combined now provide a consistent understanding of the formaldehyde-S(1V) system over a wide range of pH. Registry No. HMS, 75-92-3; HCHO, 50-00-0; HSOC, 15181-46-1.
+
~~
~~
~
(20) Boyce, S. D.; Hoffmann, M. R. J . Phys. Chem. 1984,88,4740-46.
(19) Skrabal, A.; Skrabal, R. Monatsh. Chem. 1936, 69, 11-41.
Effect of Solvent upon Anlon Radical Solvation Enthalpies Gerald R. Stevenson* and Ramli Tamby Hashim Department of Chemistry, Illinois State University, Normal, Illinois 61 761 (Received: September 24, 1985; In Final Form: February 19, 1986)
A new calorimetric technique is described for the direct measurement of relative solution electron affinities. This technique involves the measurement of the heat of reaction of the solvated anion radical with a solution of Iz in the same solvent that is hosting the anion radical [A'-,Na+(solv) + 1/212(solv) A(solv) + Na+,I-(solv)]. The enthalpy of this reaction has been placed into a thermochemical cycle to yield both the enthalpy of solvation [A'-(g) + Na+(g) A'-,Na+(solv)] and the enthalpy of generation [Na(s) A(solv) A'-,Na+(solv)] of the naphthalene anion radical in several solvent systems. It was found that the solvation enthalpy only varies by about 11 kcal/mol, going from the best solvents (hexamethylphosphoramide and = -1 79 kcal/mol), which yield unassociated ions and loose ion pairs, to the poorest solvent dimethoxyethane, AHosOlv (tetrahydropyran, AHosolv = -168 kcal/mol), which hosts only very tight ion pairs. The heats of generation (AHogen) vary (AP,, = -23 kcal/mol by the same amount, but this 11 kcal/mol difference is a much more significant percentage of in hexamethylphosphoramide). The benzophenone ketyl has a heat of solvation that is almost identical with that of the naphthalene anion radical system in tetrahydrofuran. However, it has a much more exothermic generation (-22 kcal/mol as compared to -14 kcal/mol in tetrahydrofuran), which is due primarily to the larger electron affinity of benzophenone.
+
-
Introduction The gas-phase alkali metal salts of organic anion radicals are inherently unstable relative to the metal and hydrocarbon in their standard States. For example, the heat of generation of W-Phase sodium naphthalenide from the metal and the hydrocarbon in their 0022-3654/86/2090-3217$01.50/0
-
-
standard states can be calculated from the two heats of sublimation,' the ionization potential of Na,2 and the electron affinity (1) (a) Hicks, W. T. J . Chem. Phys. 1963, 38, 1873. (b) Cox, J. D.; Pilcher, G . Thermochemistry of Organic and Organometallic Compounds; Academic: New York, 1970.
0 1986 American Chemical Society
3218
The Journal of Physical Chemistry, Vol. 90, No. 14, 1986
(EA) of naphthalene4 as shown in Scheme I.
TABLE I: Enthalpies of Reaction at 25 O C in kcal/mol reaction
SCHEME I
- + + + Na(s)
Na(g)
Na(s)
e-(g)
NP(s)
A H o = f25.9 kcal/mol
e-(g)
AHo = +118.4 kcal/mol
NP(g)
NP(s)
NP(g)
no.
Na(g)
Na+(g)
-+
(2)
AHo = +17.4 kcal/mol
(3)
AHo = -3.5 kcal/mol
(4)
NP'-(g)
+ Na+(g)
NP'-(g)
(1)
AHo = +158.2 kcal/mol (5)
On the other hand, in appropriate solvent systems, the generation of the solvated ions from the metal and naphthalene in their standard states (in the given solvent) is exothermic and produces stable solutions of the anion radical salt, reaction 6. The same Na(s)
+ NP(so1v)
-
NP'-,Na+(solv)
AHogen (6)
reaction to produce the gas-phase ions is not thermodynamically allowed (AGO >> 0 ) . Further, this reaction takes place in only a few select solvent systems. For example, in diethyl ether (DEE) reaction 6 takes place only to form minute concentrations of tight ion pairs,5 while in tetrahydrofuran (THF) concentrated solutions (0.5 M) of the anion radical can be readily formed at room temperature.s Apparently relatively small changes in the structure of the solvent result in dramatic changes in the concentrations of the anion radicals that can be formed via reaction 6. This can be either an entropy or an enthalpy effect. Even though we are severely limited in the number of solvent systems that can be used to form concentrated solutions of hydrocarbon anion radicals (protic solvents cannot be used), we were motivated to determine how the heat of reaction 6 and the solvation enthalpy of sodium naphthalenide vary with the choice of solvent by determining the heats of reaction 6 in tetrahydrofuran (THF), dimethoxyethane (DME), tetrahydropyran (THP), and hexamethylphosphoramide (HMPA). The first two of these solvents are the most common solvent systems for anion radicals and solvate the anion radicals as ion-associated pairs.6 On the other hand, hydrocarbon anion radicals exist as unassociated solvated ions in HMPA. Thus the solvation characteristics of T H F and DME are quite different than those of HMPA. These new enthalpies can be compared to that obtained in a solvent system where only intermediate amounts of anion radical can be formed (THP). In recent years we have developed a calorimetric technique that can be utilized to evaluate solvation enthalpies of hydrocarbon anion radicals.'-I0 This technique involves measuring the heat of reaction of the solvated anion radical salt with water to produce the neutral hydrocarbon, hydrogenated hydrocarbon, and aquated alkali metal hydroxide, reaction 7. NP'-,Na+(solv)
Stevenson and Hashim
+ HzO(l)
-+
'/,NP(s)
'/*NPHZ(s) + NaOH(aq) (7)
The enthalpy of reaction 7 (AH,') can be combined with the heat of reaction of sodium with water, the heat of sublimation of sodium metal, the ionization potential of sodium, the heat of (2) Lotz, W. J. Opt. SOC.Am. 1967, 57, 873. (3) Becker, R. S.; Chen, E. J . Chem. Phys. 1966, 45, 2403. (4) Szwarc, M. In Ions and Ion Pairs in Organic Reactions; Szwarc, M., Ed.; Wiley-Interscience: New York, 1974; Vol. 2, p 56, 57. ( 5 ) Stevenson, G. R. Magn. Reson. Reo. 1980, 6, 209. (6) Lee, L.; Adams, R. Jagur-Grodziniski, J.; Szwarc, M . J . Am. Chem. SOC.1971, 93, 4149. (7) Stevenson, G.R.; Schock, L. E.; Reiter, R. C. J . Phys. Chem. 1983, 87, 4004. ( 8 ) Stevenson, G. R.; Williams, Jr., E. J. Am. Chem. SOC.1979, 101, 5910. (9) Stevenson, G.R.; Chang, Y . J . Phys. Chem. 1980,84, 2265. (10) Stevenson, G. R.; Schwk, I.. E.; Reiter, R. C. J . Phys. Chem. 1984, 88, 5417
12 13 13 13 14 14 14 15 15 15 15 15 16 16 17 17 18 19
solvent THF DME HMPA THF DME HMPA THP THF THF DME HMPA
organic (A)
metal
(M) Na
Na Na
Na NP NP
BZO NP NP NP
BZO NP
BZO Na Na
AH0
ref
-68.84 +4.2 f 0.2 +4.1 f 0.2 -15.0 f 0.2 -2.4 f 0.5 -0.3 f 0.1 -7.0 f 0.2 +2.4 f 0.1 +2.7 f 0.1 +2.1 f 0.1 +2.2 f 0.1 +3.5 f 0.1 -17.4 -22.7 +3.2 +14.7 -25.9 -118.4
14b this work this work this work this work this work this work this work this work this work this work this work 7 14a 7 15 16
17
hydrogenation of the hydrocarbon, the heat of sublimation of the hydrocarbon, and the electron affinity of the hydrocarbon to yield the solvation enthalpy of the anion radical salt." For the naphthalene-sodium system, this solvation enthalpy (AHosolv)is given by AHosolv= -AH7' - 203.9 in kcal/mol.I2 This calorimetric technique requires that the solvated anion radical and the solvent both be exposed to a large excess of water in the calorimeter. For this reason, the heat of aquation of the solvent must first be subtracted from the measured heat to obtain the heat due to reaction 7. Part of the purpose of this report is to describe a more direct calorimetric technique for determining solvation enthalpies, where the result is not a relatively small difference between two large numbers (Le., heat of aquation of the solvent and the total heat measured). Furthermore, this new technique does not require knowledge of the heat of hydrogenation of the substrate or even the structure of the Birch reduction product. Thus, it is applicable to non-hydrocarbon anion radicals. Our calorimetric technique cannot be utilized when T H P serves as the solvent due to the fact that only low concentrations of hydrocarbon anion radicals can be generated in this solvent. However, Szwarc and co-workers4 were able to measure the equilibrium constant of reaction 8 as a function of temperature and obtain the thermoNa(s)
+ NP(THP)
-
AHo = -12.0 kcal/mol
NP'-,Na+(THP)
(8)
So = -41 eu
dynamic parameters for the generation of the anion radical salt from the metal and the solvated naphthalene. Thus, with some new calorimetrically determined heats of solvation we hoped to have the heats of reaction 6 and the solvation enthalpy of sodium naphthalenide ( A H o for reaction 9) in four NP'-(g)
+ Na+(g)
-
NP'-,Na+(solv)
AHo,,,,
(9)
very different solvent systems and some insight as to how changes in the solvent affect the enthalpy of solvation of hydrocarbon anion radicals. Experimental Section The anion radicals were generated via the reduction of the organic substrate on a freshly distilled alkali metal mirror as previously described.' The anion radical solutions were then sealed into glass bulbs under high The energies of the solvated anion radicals were obtained via two different calorimetric techniques (reaction with water and reaction with I*). (1 1) The best literature values for all of these constants have been collected and tabulated in ref 7 . (12) The value -203.9 represents a combination of all of the appropriate constants and can be obtained by simply placing the proper values for the EA, heat of sublimation, and heat of hydrogenation into eq 5 of ref 7. (13) Stevenson, G. R.; Zigler, S. S.;Reiter, R. C. J . Am. Chem. SOC.1981, 103, 6057.
The Journal of Physical Chemistry, Vol. 90, No. 14, 1986 3219
Anion Radical Solvation Enthalpies TABLE 11: Enthalpies of Reaction in kcal/mol solvated ions" solvent [Ny-,Na+ltight THP [NP'-,Na+ltig~,t THF [NP'-,Na+Il,, DME NP'- + Na+ HMPA [NP'-,Na+l lrn5 THF [BZO'-,Na+ltight THF
AH'Wivb -168.2 f 1.0 -170.0 i 1.9 -179.4 f 1.4 -178.1 f 1.8 -176.9 f 1.5
AH,"
AH"... -12.0 f 1.0 -14.2 f 1.9
Afflll"
-3 1.4 f 0.9 -30.3 f 1.9
-59.1 f 1.4 -48.1 f 1.2
-23.1 f 1.4 -23.1 f 1.8 -21.1 f 1.5 -22.1 f 1.6
-45.2 f 1.5 -51.2 f 1.2
-172.3 f 1.7
a We are using the tight-loose symbolism, which is utilized in Szwarc's book," as opposed to the A'-,Na+ - A'-,S,Na+ symbolism. *These enthalpies were caiculatedfrom AHl;" as shown in Scheme 11.
120
propriate solvent in our calorimeter system, Table I. The change in the heat content of the calorimeter was considered to be due to the dissolution of the organic substrate. Since all of our enthalpies come from linear plots, the errors reported in Tables I and I1 represent standard deviations in the slopes of these lines.
-
calories
0
L 1
0
3
2
4
millimoles o f salt
Figure 1. Plots of the change in the heat content of the calorimeter vs. the millimoles of solvated anion radical salt in the glass bulbs. The change in the heat content of the calorimeter is equal to the heat capacity of the calorimeter parts plus that of the 100 mL of solvent containing the I2 multiplied by the change in the temperature due to reaction 10. The slopes of these lines are equal to the enthalpies of reaction 10.
Reaction with Water. The evacuated glass bulbs containing the anion radical solutions were broken under 100 mL of water in a modified Parr solution calorimeter.8 The output of the calorimeter was directed to a MINC I1 64 K computer by Digital as previously described.I3 The heat of aquation of the solvent was subtracted from the heat of reaction of the anion radical solution with the water to yield the enthalpy for reaction 7. Reaction with Iodine. The glass bulbs containing the solvated anion radical [A'-,Na+(solv)] were broken under 100 mL of the same solvent used to solvate the anion radical but containing 0.6 g of I> The calorimeter was charged with freshly distilled solvent containing the I> The calorimeter system was continuously purged with N 2 prior to and during the reaction. The reaction products consisted of solvated alkali metal iodide and solvated organic J ~calosubstrate, reaction 10. As in our previous s t ~ d i e s , ' ~the A'-,Na+(solv)
-
+ 1/212(s01v)
A(so1v)
+ I-,Na+(solv)
Results and Discussion Crushing the evacuated glass bulbs containing the sodium naphthalene anion radical salt in THF, DME, or HMPA under 100 mL of the same solvent containing 0.6 g of I2results in a rise in the temperature of the calorimeter. Plots of the change in the heat content of the calorimeter vs. the millimoles of anion radical in the bulbs were generated, and they proved to be linear, Figure 1. These data could not be used to calculate the anion radical solvation enthalpies and the heats of anion radical generation until the heats of solution of 12,NaI, and the organic substrate (A) were evaluated. These data are reported in Table I, which is coupled Na+(g) to Scheme 11. The solvation enthalpies for NP'-(g) and heats of generation (AHogen)of the solvated anion radicals were calculated as shown in Scheme I1 and the data are reported in Table 11.
+
-
SCHEME I1 A'-,Na+(solv)
+ '/212(s01v) I-,Na+(solv) + A(so1v) l/J2(s) + Na(s) NaI(s)
A(so1v)
(14) (a) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic: New York, 1970; p 219. (b) Suttle, J. F. "The Alkali Metals". In Comprehensiue Inorganic Chemistry; Sneed, C., Brasted, R. C., Ed.; Van Norstand: New York, 1957; Vol. VI. (15) Caldwell, G . ;Kebarle, P. J . Chem. Phys. 1984, 80, 577. (16) Hicks, W. T. J . Chem. Phys. 1963, 38, 1873. (17) Lotz, W. J . Opt. Soc. Am. 1967, 57, 873.
+ AHlz'
A*-(g)
Na(g)
(14)
A'-,Na+(solv) - 72AH13'
-
A(g)
+ AHI4'
A(so1v)
(15)
Ab)
(16)
+ e-(d
Na(s)
Na+(g) + e - ( d
Na(g)
+ Na+(g)
A'-,Na+(solv)
A'-(g)
(12) (13)
I-,Na+(solv)
A(s)
AH'solv
I*(solv)
+ Na(s)
AHogen = -AH,,'
(10)
rimeter output was fed directly into the computer system. However, with reaction 10 as opposed to reaction 7, the temperature rise in the calorimeter was due to only one reaction, since the calorimeter was charged with the same solvent containing the iodine as the anion radical solvent. Thus, a correction analogous to that accounting for the aquation of the solvent (described above) need not be made. Any water or other protic impurity in the solvent placed in the calorimeter would lead to some Birch reduction products. N M R analysis of the calorimeter contents did not indicate the presence of hydrogenated substrate. All of the solvents were freshly distilled from potassium metal prior to placing them into the calorimeter. The heats of solution of NaI, naphthalene, and benzophenone in the various solvents were determined by simply breaking sealed bulbs containing these neutral organic substrates under the ap-
--
I2(s) NaI(s)
-
-
(1 1)
(17) (18) (19)
= AHogen AHIS'
+
+ AH16' + AH,," + Aff18' + AH19' When the solvation enthalpy of NP'- + Naf in THF was
determined by reacting the solvated anion radical with water, reaction 7, a value of -172.5 f 4.0 kcal/mol was reported.8 The value obtained via the reaction with I2 (reaction 10) yields a value (Table 11) that is well within experimental error of this previously reported value. In addition, the new technique leads to a smaller experimental error. In order to lend more support to the new experimental technique described here, we crushed a series of bulbs containing NP'-,Na+ in DME under water in our calorimeter. A plot of the change in heat of the calorimeter vs. the millimoles of anion radical in the bulbs is linear; and when the slope of this line (AH,' = -30.3 f 1.9 kcal/mol) is subtracted from -203.9 as described in the Introduction, a solvation enthalpy of -173.6 3.9 kcal/mol is obtained. Again, the value obtained via reaction
*
3220 The Journal of Physical Chemistry, Vol. 90,No. 14, 1986
-
-
115.2 178. 158.5
170.0 179.4 NPlql
+
Na(s1
Stevenson and Hashim this, the solvation enthalpy of the unassociated gas-phase ions to yield the loose ion pairs in T H F must be -170.0 - 6.9 kcal/mol, Table 11. This is well within experimental error of the values obtained in DME and HMPA. The free solvated ions exist in HMPA because it is a better solvent than THF. However, the solvation enthalpy of the dissociated ions is similar in T H F to what it is in HMPA. The same absolute difference in AHosolv is seen in AHogen but it represents nearly a 50% change, whereas in AZ3°solv in AHogen it represents only a 5 4 % change. When these changes in the heat of generation with solvent are coupled with the more negative entropies of generation in the poorer solvents, it renders the anion radical less thermodynamically stable relative to neutral molecule and sodium metal in solvents like DEE. It appears that the naphthalene anion radicals Na+ solvation enthalpies vary only to a small degree with the choice of the solvent, but its maniis relatively large, Figure 2. festation in AHogen In previous the solvation enthalpies of a number of polyaromatic hydrocarbon anion radicals have been reported in THF with sodium serving as the cation, and it was found that the solvation enthalpy varied less than 7% as the anion radical was varied from naphthalene (the smallest) to perylene (the l a r g e ~ t ) . ~ Now we find, Table 11, that even a drastic change in the nature of the anion radical, from a hydrocarbon anion to a ketyl, has no appreciable effect upon the solvation enthalpy. Even though the Na+ and NP'- Na' are very solvation enthalpy of BZ0'similar, the heats of generation of the two anion radicals in T H F are very different. The greater exothermicity of generation of the BZO'-,Na+ system is entirely due to the greater electron affinity of benzophenone relative to that of naphthalene. The predominate force in controlling the relative heats of generation of organic anion radicals in THF appears to be the electron affinity of the substrate. Except for our preliminary communi~ation,'~ this is the first report of anion radical solvation enthalpies measured by means other than their reaction with water. This new calorimetric technique makes use of reaction 10 as opposed to reaction 7 and is more facile and results in less error. Further, the new method can be used to study non-hydrocarbon anion radicals, and it can be extended to solvent systems that have very exothermic heats of aquation like HMPA.
+
Figure 2. Energy diagram for the naphthalenesodium system interacting with several solvents. All of the energy differences are given in kcal/mol. The energy differences between the solid metal plus solid naphthalene and the solvated anion radical salts are obtained by simply summing the heats of generation and the heats of solution of naphthalene.
10 contains less error but is still within experimental error of that obtained when reaction 7 is used (see Table 11). It has been observed that the anion radical forms only tight ion pairs ( [NP*-,Na+llight)in THP and loose ion pairs ([NP'-,Na+II,) in DME,'* while in T H F a mixture of tight and loose ion pairs is observed.'* Thus, it appears that the solvation enthalpy is more negative for solvent systems that yield looser ion pairs. The results in HMPA are consistent with this trend. This is the case, since the anion radical and sodium cation are free of ion association in HMPA, and the solvation enthalpy of Na' + NP'is almost identical with that in DME. In THF the loose ion pair is found to be 6.9 kcal/mol lower in energy than the tight ion pair for the following r e a c t i ~ n : ~ , ' ~ [NP'-,Na+Itight+ [NP'-,Na+]loose
AHo = -6.9 kcal/mol
at 25 OC.18 The equilibrium constant for this reaction is 1 X Thus, all but one percent of the N P anion radicals used in our calorimetry experiment (in THF) were tight ion pairs. Based on (18)
53, 326.
Karasawa, Y . ;Levin, G.; Szwarc, M. Proc. R. SOC.London A , 1971,
+
+
Acknowledgment. We thank The National Science Foundation (Grant No. CHE-8411827) for support of this work. Registry No. THF, 109-99-9; DME, 110-71-4; HMPA, 680-31-9; BZO,119-61-9; NP, 91-20-3; NaI, 7681-82-5. (19) Stevenson, G. R.; Hashim, R. T. J. Am. Chem. SOC.1985,107,5794.
